dtbmv.f(3)

NAME
dtbmv.f -

SYNOPSIS

  Functions/Subroutines
subroutine dtbmv (UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX)
DTBMV

Function/Subroutine Documentation

  subroutine dtbmv (characterUPLO, characterTRANS, characterDIAG, integerN, integerK, double precision, dimension(lda,*)A, integerLDA, double precision, dimension(*)X, integerINCX)

DTBMV Purpose:

     DTBMV  performs one of the matrix-vector operations
        x := A*x,   or   x := A**T*x,
     where x is an n element vector and  A is an n by n unit, or non-unit,
     upper or lower triangular band matrix, with ( k + 1 ) diagonals.

Parameters:
    UPLO

              UPLO is CHARACTER*1
               On entry, UPLO specifies whether the matrix is an upper or
               lower triangular matrix as follows:
                  UPLO = 'U' or 'u'   A is an upper triangular matrix.
                  UPLO = 'L' or 'l'   A is a lower triangular matrix.

    TRANS

              TRANS is CHARACTER*1
               On entry, TRANS specifies the operation to be performed as
               follows:
                  TRANS = 'N' or 'n'   x := A*x.
                  TRANS = 'T' or 't'   x := A**T*x.
                  TRANS = 'C' or 'c'   x := A**T*x.

    DIAG

              DIAG is CHARACTER*1
               On entry, DIAG specifies whether or not A is unit
               triangular as follows:
                  DIAG = 'U' or 'u'   A is assumed to be unit triangular.
                  DIAG = 'N' or 'n'   A is not assumed to be unit
                                      triangular.

    N

              N is INTEGER
               On entry, N specifies the order of the matrix A.
               N must be at least zero.

    K

              K is INTEGER
               On entry with UPLO = 'U' or 'u', K specifies the number of
               super-diagonals of the matrix A.
               On entry with UPLO = 'L' or 'l', K specifies the number of
               sub-diagonals of the matrix A.
               K must satisfy  0 .le. K.

    A

              A is DOUBLE PRECISION array of DIMENSION ( LDA, n ).
               Before entry with UPLO = 'U' or 'u', the leading ( k + 1 )
               by n part of the array A must contain the upper triangular
               band part of the matrix of coefficients, supplied column by
               column, with the leading diagonal of the matrix in row
               ( k + 1 ) of the array, the first super-diagonal starting at
               position 2 in row k, and so on. The top left k by k triangle
               of the array A is not referenced.
               The following program segment will transfer an upper
               triangular band matrix from conventional full matrix storage
               to band storage:
                     DO 20, J = 1, N
                        M = K + 1 - J
                        DO 10, I = MAX( 1, J - K ), J
                           A( M + I, J ) = matrix( I, J )
                  10    CONTINUE
                  20 CONTINUE
               Before entry with UPLO = 'L' or 'l', the leading ( k + 1 )
               by n part of the array A must contain the lower triangular
               band part of the matrix of coefficients, supplied column by
               column, with the leading diagonal of the matrix in row 1 of
               the array, the first sub-diagonal starting at position 1 in
               row 2, and so on. The bottom right k by k triangle of the
               array A is not referenced.
               The following program segment will transfer a lower
               triangular band matrix from conventional full matrix storage
               to band storage:
                     DO 20, J = 1, N
                        M = 1 - J
                        DO 10, I = J, MIN( N, J + K )
                           A( M + I, J ) = matrix( I, J )
                  10    CONTINUE
                  20 CONTINUE
               Note that when DIAG = 'U' or 'u' the elements of the array A
               corresponding to the diagonal elements of the matrix are not
               referenced, but are assumed to be unity.

    LDA

              LDA is INTEGER
               On entry, LDA specifies the first dimension of A as declared
               in the calling (sub) program. LDA must be at least
               ( k + 1 ).

    X

              X is DOUBLE PRECISION array of dimension at least
               ( 1 + ( n - 1 )*abs( INCX ) ).
               Before entry, the incremented array X must contain the n
               element vector x. On exit, X is overwritten with the
               tranformed vector x.

    INCX

              INCX is INTEGER
               On entry, INCX specifies the increment for the elements of
               X. INCX must not be zero.

Author:
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Date:
    November 2011

Further Details:

      Level 2 Blas routine.
      The vector and matrix arguments are not referenced when N = 0, or M = 0
      -- Written on 22-October-1986.
         Jack Dongarra, Argonne National Lab.
         Jeremy Du Croz, Nag Central Office.
         Sven Hammarling, Nag Central Office.
         Richard Hanson, Sandia National Labs.

Definition at line 187 of file dtbmv.f.

Author

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